Question: Simplify; express your answer in exponential form. Assume $n\neq 0, x\neq 0$. $\dfrac{{(n)^{5}}}{{(n^{-2}x^{2})^{-3}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${n}$ to the exponent ${5}$ . Now ${1 \times 5 = 5}$ , so ${(n)^{5} = n^{5}}$ In the denominator, we can use the distributive property of exponents. ${(n^{-2}x^{2})^{-3} = (n^{-2})^{-3}(x^{2})^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(n)^{5}}}{{(n^{-2}x^{2})^{-3}}} = \dfrac{{n^{5}}}{{n^{6}x^{-6}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{5}}}{{n^{6}x^{-6}}} = \dfrac{{n^{5}}}{{n^{6}}} \cdot \dfrac{{1}}{{x^{-6}}} = n^{{5} - {6}} \cdot x^{- {(-6)}} = n^{-1}x^{6}$.